$\dfrac{ -10t - 6u }{ -9 } = \dfrac{ 5t - 6v }{ -10 }$ Solve for $t$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -10t - 6u }{ -{9} } = \dfrac{ 5t - 6v }{ -10 }$ $-{9} \cdot \dfrac{ -10t - 6u }{ -{9} } = -{9} \cdot \dfrac{ 5t - 6v }{ -10 }$ $-10t - 6u = -{9} \cdot \dfrac { 5t - 6v }{ -10 }$ Multiply both sides by the right denominator. $-10t - 6u = -9 \cdot \dfrac{ 5t - 6v }{ -{10} }$ $-{10} \cdot \left( -10t - 6u \right) = -{10} \cdot -9 \cdot \dfrac{ 5t - 6v }{ -{10} }$ $-{10} \cdot \left( -10t - 6u \right) = -9 \cdot \left( 5t - 6v \right)$ Distribute both sides $-{10} \cdot \left( -10t - 6u \right) = -{9} \cdot \left( 5t - 6v \right)$ ${100}t + {60}u = -{45}t + {54}v$ Combine $t$ terms on the left. ${100t} + 60u = -{45t} + 54v$ ${145t} + 60u = 54v$ Move the $u$ term to the right. $145t + {60u} = 54v$ $145t = 54v - {60u}$ Isolate $t$ by dividing both sides by its coefficient. ${145}t = 54v - 60u$ $t = \dfrac{ 54v - 60u }{ {145} }$